Elastic and electrical properties are among the most valuable geophysical information that the oil industry has been using to characterize the earth's subsurface in the exploration and development of hydrocarbon reservoirs. By elastic properties, it is meant the behavior of the medium associated with the reversible deformation under stress or strain, e.g., seismic velocity. By electrical properties, it is meant the behavior of the medium associated with the presence and flow of electric charge, e.g., resistivity or conductivity. In hydrocarbon exploration, these two types of properties are mainly derived from seismic, controlled-source electromagnetic (CSEM), and well data. While seismic data remain the major source of information for oil exploration, electromagnetic (EM) data have generated growing interest because of their sensitivity to variation in fluid saturation, thus enabling the discrimination between water, which is more conductive, and hydrocarbons, which are more resistive.
Rocks are generally considered as compositions of different types of minerals with fluids contained in the pore spaces. Hence, geophysical response (seismic, electromagnetic, or thermal) is primarily controlled by the interaction among various constituents such as grain minerals, cements, pore spaces, and fluids. Rock physics models provide crucial links between the microscopic rock properties and macroscopic physical responses such as seismic velocity and resistivity. Though it is not practical and in fact impossible to include all factors in a rock physics model, some key rock parameters can be identified, including mineralogy, porosity, pore structure, and fluid properties. For example, fluid properties are largely governed by temperature and pressure profiles as well as compositional environment such as salinity, API gravity, fluid saturation, gas-oil ratio (GOR), and gas gravity. Pore structure, such as shape, orientation and connectivity, largely influences the overall anisotropy of seismic velocity and resistivity. Hence, a consistent rock physics model helps to better understand the relationship between the rock parameters and the overall geophysical responses. It further implies that one type of physical response can be derived from other types of response given appropriate rock physics relationship and sufficient information about rock parameters.
Seismic anisotropy has been widely observed in the earth's subsurface. For example, shale comprises significant volume of the elastic fill of sedimentary basins, and produces transverse isotropy (TI), which is the most common type of anisotropy. Furthermore, many hydrocarbon reservoirs are relatively deep and have undergone tremendous overburden forces as well as local stresses. In many cases, such forces exceed the strength of the rocks and open up fractures in the rocks, resulting in stress-induced anisotropy. Depending on the number of fracture sets and fracture orientation, anisotropy varies from HTI (transverse isotropy with horizontal symmetry axis), orthorhombic, to the even more complicated monoclinic or triclinic type. From the rock physics point of view, seismic anisotropy can result from preferred alignment of mineral grains and pore spaces, from preferred direction of fluid flow among pore spaces, and from intrinsic seismic anisotropy of minerals.
Early observations of resistivity anisotropy were noted by the discrepancy between surface measurements in different directions. Similar to velocity, resistivity anisotropy may result from preferred orientation of mineral grains and pore spaces, from preferred direction of current flow among pore spaces, and from intrinsic resistivity anisotropy. Since resistivity is sensitive to fluid type, spatial distribution of fluids in the rocks also contributes to the effective resistivity anisotropy. In a vertical well that penetrates horizontal bedding layers, vertical resistivity from cross-dipole measurements is always at least as much as, if not greater than, horizontal resistivity. It is important to know that elasticity is represented by a fourth-rank tensor while resistivity is represented by a second-rank tensor, which means that resistivity anisotropy may have simpler mathematical forms, e.g., isotropy, transverse isotropy, and orthorhombic symmetry.
Many existing theoretical rock physics models are devoted to seismic velocity anisotropy (e.g., Brown and Korring a, 1975; Hamby et al., 1994; Xu and White, 1995; Thomsen, 1995; Pointer et al., 2000) and the isotropic seismic-to-resistivity transformation (e.g., Bristow, 1960; Sen et al., 1981; Kachanov et al., 2001; Hacikoylu, 2006). However, very few studies have been found on resistivity anisotropy itself (e.g., Wang, 2006) and the transformation between velocity and resistivity anisotropy. Carcione et al. (2007) discussed possible ways of combining constitutive equations of different physical properties to obtain relationship between seismic and electrical properties. For example, Archie's law for resistivity combined with the Gassmann equation or the time-average equation are two possible choices. Rock physics models cited by Carcione et al. (2007) may be basically applied to sand-shale sequences and are not directly applicable to more complicated cases such as fractured and carbonated rocks. Moreover, no discussion is provided for partial saturation cases, which is commonly encountered in hydrocarbon reservoirs.
3D inversion has been widely used in EM data interpretation. It generally involves iterative forward modeling (numerically solving Maxwell's equations) and comparing to measured EM data, then updating the resistivity model for the next iteration. To start the iteration process, an initial guess of the resistivity model is needed. Current approaches for building a resistivity model generally depend on the availability of the data and the experience of the practitioners. For example, if neither seismic nor well data are available, model builders may choose a homogeneous half-space or layered model. Sometimes they use rectangular blocks and assign random values as an initial guess of the resistivity structure (Haber and Ascher, 2001). Other approaches may use the information from corresponding seismic data, e.g., constructing an initial resistivity model (sometimes called a starting model or a background model) by digitizing the horizons from seismic amplitude maps and then assigning values according to values from resistivity logs (Carazzone et al., 2005). Because 3D EM inversion is nonlinear, inversion results can be easily trapped into a local minimum (i.e., an inverted resistivity model that differs significantly from the true resistivity structure), particularly if the initial guess is not good. Thus, even when the initial guess is from seismic data, the final result from EM inversion does not always honor seismic data.
When log data are available, resistivity volumes can be constructed by linear interpolation of resistivity between well locations (Hoversten et al., 2001). This approach is based on an empirical relationship between observed well log and laboratory data. Portniaguine et al. (2006) suggest building the model from seismic impedance volumes by assuming a linear empirical relationship between seismic impedance and logarithm of conductivity. Their purpose was to build a reference model for forward modeling of EM response over hydrocarbon reservoirs. The procedure is firstly to invert the impedance from seismic data, then do a linear regression between impedance and logarithm of resistivity in a cross-plot, and finally extend such empirical relation to the whole volume.
Mendrofa and Widarsono (2007) discuss the possibility of building the seismic-resistivity relationship by first rearranging the Gassmann (1951) equation to establish the transformation between velocity and water saturation, and then converting water saturation to resistivity. However, their approach is limited to the Gassmann model and is only applicable to isotropic resistivity, which is a special case discussed by Carcione et al. (2007). Moreover, the lack of methods on how to obtain the porosity for locations away from well sites, which is a key parameter in the derivation of water saturation from velocity, limits the application of this approach to generating volumes of resistivity.
In summary, currently known approaches for resistivity modeling appear to be either empirical or semi-empirical and lack the capability to handle anisotropic resistivity, which has been frequently observed in EM data and has been shown to have significant effects on resistivity imaging. In many cases, the current methods do not provide a direct physical link between resistivity behavior and rock-fluid properties. There is a need in hydrocarbon exploration for a method that can generate 3D anisotropic resistivity volumes by incorporating information from different measurements (seismic, electromagnetic, well log, cores). Preferably, such a method should be able to quantify the uncertainty of predicted resistivity data from scenario analysis of a number of rock parameters. In certain idealized cases, such a method should provide a resistivity volume with resolution comparable to the data volumes of seismic attributes such as porosity and seismic impedance. As compared to inversion results of EM data, a resistivity volume derived from such a method should provide more details of reservoir rocks. The present invention satisfies this need.